Preheat oven to 350. Line baking sheets with parchment paper or silicone baking mats and set aside.
Cream butter and sugar. Stir in egg, vanilla and extracts until light and fluffy. Add in dry ingredients and stir until just combined. Scrape the edges of the bowl and mix again to ensure cookie dough is mixed evenly. Stir in 1/2 cup toasted coconut and the small pieces of dried pineapple. Scoop onto prepared cookie sheets and bake 8-10 minutes until cookies have spread and edges have become lightly golden. Cool on baking sheet 3 minutes before transferring to cooling rack.
For the glaze, stir powdered sugar with rum extract and milk until it's the consistency of elmer's glue {I know, not the best visual!}. Drizzle over cookies and top with remaining toasted coconut and maraschino cherries if desired.